An uncertain solution by lavalyn:
The sequence from to
yields a ko for life. Black cannot connect without removing the white stones because of shortage of liberties.
To avoid the ko is impossible - here, White falsifies an eye so Black is left a cyclops.
Again avoiding the ko yields only death for Black.
The throw-in here doesn't work - the marked point will become a real eye for the corner group, so the two disconnected black groups will have one real eye each and a shared eye - and thus live.
A similar result occurs if White approaches from the side.
is a mistake